CIRCULAR WAVEGUIDE WITH INHOMOGENEOUS DIELECTRIC 1245 



and if tan v? = 5 X 10^^, the dicleftric loss in a 90° bond is a])oiit 0.25 

 db. 



2.4 Can Dissipation Be Used to Discourage Spurious Modes? 



It was shown in Section 2.1 that the effect of markedly increasing the 

 attenuation constant of one of two coupled transmission lines is to re- 

 duce the over-all attenuation of a wave introduced on the other line. 

 One might wonder whether it would be practicable to decrease the per- 

 missible radius of a compensated bend by introducing loss into the 

 spurious modes. The answer is "No", at least for guides large enough to 

 propagate 200 to 300 modes at the operating wavelength. One simply 

 cannot get the required magnitude of loss into the spurious modes with- 

 out simultaneously introducing intolerable loss into TEoi . A numerical 

 example will make this clear. 



We found in Section 2.3.3 that with a three-sector compensator in 

 2-inch guide at 5.4 mm it would be possible to negotiate a bend of 

 radius about 12 feet with a maximum loss of 0.1 db by mode conversion 

 to TEi2 (the worst spurious mode). Let us now ask w^hat the attenuation 

 constant of TE12 would have to be if we wished to transmit around a 

 bend of radius 6 feet with a three-sector compensator, and have the 

 mode conversion loss suffered by TEoi not greater than 0.1 db in a 90° 

 bend. Preparing to substitute into (80) of Section 2.1, M'e have the 

 following values: 



'to 



6 = 72 inches, 



K[i2] = C[i2] + f/[i2] = 2.54/6 = 0.0353 in"\ 



z — 7r6/2 = 113.1 inches, 



/3o — ^1 ^ /io — hi = 0.236 radians/inch, 



N = 0.1 db = 0.0115 nepers. 



From (80) we get 



«[i2] — «[oi] = 12.2 nepers/inch ^ 4200 db/meter. 



Since the maximum TE12 attenuation which can be achieved in a 2-inch 

 guide by a mode filter which transmits TEoi freely is of the order of 10 

 db/meter,* the value of a[n] called for by the above calculation is ob- 

 viously out of the question. 



* This estimate is based on calculations described in Reference 6 for modes in 

 a helix surrounded by a lossy sheath; but it is doubtful that much greater loss 

 could be produced by other types of filter, such as resistance card "killers". 



